Question

You have $5,000 down payment on a $20,000 car. The dealer offers you the following two options:

(a) paying the balance with end-of-month payments over the next five years at

?^(12) = 9%.

(b) a reduction of $1000 in the price of the car, the same down payment of $5,000, and bank financing of the balance after down payment, over 5 years with end-of- month payments at ?^(12) = 12%.

Which option is better and why? (DO NOT USE EXCEL)

Answer 1

Formula for EMI is:

EMI = [P x r x (1+r) ⁿ]/ [(1+r) ⁿ-1

P = Loan amount or principal

r = Interest rate per month

n = Number of monthly installments

Computation of EMI for option (a)

P = $ 20,000 - $ 5,000 = $ 15,000

r = 0.09/12 = 0.0075 p.m.

n = 5 years x 12 months = 60

EMI = [$ 15,000 x 0.0075 x (1+0.0075)⁶⁰]/ [(1+0.0075)⁶⁰- 1]

      = [$ 15,000 x 0.0075 x (1.0075)⁶⁰]/ [(1.0075)⁶⁰- 1]

      = ($ 15,000 x 0.0075 x 1.56568102694157)/ (1.56568102694157 – 1)

      = ($ 15,000 x 0.0075 x 1.56568102694157)/0.56568102694157

      = $ 176.139115530927/0.56568102694157

      = $ 311.375328395307 or $ 311.38

Total payments = $ 311.38 x 60 = $ 18,682.80

Computation of EMI for option (b)

P = $ 20,000 - $ 5,000 - $ 1,000 = $ 14,000

r = 0.12/12 = 0.01 p.m.

n = 5 years x 12 months = 60

EMI = [$ 14,000 x 0.01 x (1+0.01)⁶⁰]/ [(1+0.01)⁶⁰- 1]

      = [$ 14,000 x 0.01 x (1.01)⁶⁰]/ [(1.01)⁶⁰- 1]

      = ($ 14,000 x 0.01 x 1.81669669856409)/ (1.81669669856409– 1)

      = ($ 14,000 x 0.01 x 1.56568102694157)/0.81669669856409

      = $ 254.337537798973/0.81669669856409

      = $ 311.422267588625 or $ 311.42

Total payments = $ 311.42 x 60 = $ 18,685.20

Both options are almost same in term of EMI but total payment for option (a) is less than option (b)

Hence option (a) seems to be better.